Pugging lanky Manila mango tree.

[NewGen]

My Manila has 4 really long branches, I recently cut down 2 of them, those 2 are sprouting new growths.
I left the remaining 2 branches on because they're loaded with fruits. I like Manila mangoes, very fragrant and sweet.  I intend to cut them down as well, after harvesting the fruits in September.
Question: how long should I expect to wait to get fruits again, 2 years? 3 years?
Thanks,